Dynamical behavior of a one-prey two-predator model with random perturbations

• A stochastic one-prey two-predator model where the growth rate of two predators is negative is thoroughly investigated.
• Persistence and extinction properties for the concerned stochastic model are studied in detail.
• Existence of stationary distribution under certain parametric restrictions is proved.
• Global asymptotic stability for solutions of stochastic model is also proved.
• Finally, analytical findings are validated with the help of some numerical examples.

The objective of this paper is to systematically study the qualitative properties of a stochastic one-prey two-predator model. We have derived sufficient conditions (parametric restrictions) for extinction of each species and at the same time we also notice that when one or two species go extinction, remaining species can be stable in time average under same parametric restrictions, i.e., extinction of one or two species ensures about the stability in mean of other species. Next, we have proved that the system admits a stationary distribution under some simple parametric conditions, which can be considered as a stability of the system in weak sense. Finally, we have proved that system is globally asymptotically stable.